need help with a motion question?
A 70 kg fisherman is quietly fishing in a 40 kg dinghy at rest on a lake when suddenly he is attacked by a swarm of wasps. To escape, he leaps into the water and exerts a horizontal force of 140 N on the boat. If the force on the fisherman lasted for 0.50 secs, determine the initial speed attained by both the man and the boat.
Hi!
Initial speed is actually equal to 0, because he’s at rest initially.
However, after 0.5 seconds… (if that’s what you mean by initial speed)
Then, the fisherman exerts a 140N force on the dinghy horizontally.
So, by Newton’s second law of motion,
F = ma
140N = 70*a, where we calculate the acceleration achieved by the man
a = 2 m/s^2
v = a*t = 2*0.5 = 1 m/s
The man achieves a speed of 1 m/s after 0.5 seconds.
By Newton’s third law of motion,
Every action has an equal and opposite, collinear reaction.
Therefore, the boat is moves forward with 140N worth of force in the opposite direction of the man
140N = 40*a
a = 3.5 m/s^2
v = a*t = 3.5*0.5 = 1.75 m/s
The boat achieves a speed of 1.75 m/s after 0.5 seconds.
Dinghy Crab Fishing 07/10/2011
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